Question

if the median AD to the side BC of a triangle ABC is also an angle bisector of angle A then AB/AC is _____

Answer 1

In ∆ABC AD is the bisector of ∠A and E is a point on AC such that DE ∥ BA

we have ∠BAD =∠DAC or ∠BAD =∠DAE·····(1)(since AD is a bisector of ∠ A)

Again ∠ABD =∠EDC(since BC intesect DE ∥ BA)

Now in ∆ABD ∠ADC(ext· angle) =∠ABD+∠BAD (int opp. angles)

Or ∠ADE +∠EDC=∠ABD+∠BAD

Or ∠ADE +∠ABD=∠ABD+∠BAD

Or ∠ADE=∠BAD

Or ∠ADE=∠DAE (from 1 ∠BAD=∠DAE)

Now In ADE ∠ADE= ∠DAE therefore DE=EA

Answer 2

I think AB/AC=1unit

if I am correct then please mark me as a brain list